Question

When trying to determine probabilities, one must first assess whether the variable would have a normal distribution. Using the tools from this course, what are some methods that could be used to determine whether a variable has a normal distribution?

Answer 1

From the given information,

The required some methods that could be used to determine whether a variable has a normal distribution are listed below:-

1. Histogram of data

The histogram is a data visualization that shows the distribution of a variable. It gives us the frequency of occurrence per value in the dataset, which is what distributions are about.

2. Boxplot of data

The Box Plot plots the 5-number summary of a variable: minimum, first quartile, median, third quartile and maximum.

3. QQ plot of data

QQ Plot stands for Quantile vs Quantile Plot, which is exactly what it does: plotting theoretical quantiles against the actual quantiles of our variable.

4. Kolmogorov Smirnov test

The Kolmogorov Smirnov test computes the distances between the empirical distribution and the theoretical distribution and defines the test statistic as the supremum of the set of those distances.

5. Lilliefors test

The Lilliefors test is strongly based on the KS test. The difference is that in the Lilliefors test, it is accepted that the mean and variance of the population distribution are estimated rather than pre-specified by the user.

6. Shapiro Wilk test

The Shapiro Wilk test is the most powerful test when testing for a normal distribution. It has been developed specifically for the normal distribution and it cannot be used for testing against other distributions like for example the KS test.

Thank you.